This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960-1989, and \(yr\) is the measurement year (all FIA data). Free parameters are \(ge\): biomass growth enhancement over time, \(\alpha\): the growth compensation of lost plot biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.
Model selection is used to determine the best fitting models including \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period) and \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).
model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)
Note:
This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval
This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):
Below the model fitting procedure is implemented by ecoprovince:
## Error in eval(extras, data, env) : object 'P_211' not found
## Error in eval(extras, data, env) : object 'P_211' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 72677.43
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.614e-01 2.059e-01 2.726 0.00642 **
## phi 9.854e-03 6.256e-03 1.575 0.11528
## alpha 8.465e-01 2.725e-02 31.064 < 2e-16 ***
## a 4.030e+01 1.937e+00 20.805 < 2e-16 ***
## b 1.073e+02 5.001e+00 21.459 < 2e-16 ***
## c 1.144e+02 4.148e+00 27.588 < 2e-16 ***
## d 9.190e-01 3.966e-02 23.173 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4627 on 6798 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18747 6234.1
## 2 18742 6234.1 5 0.04 0.0268 0.9997
## 3 18741 5853.7 1 380.34 1217.6643 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 195208.2
## 2 2 195169.6
## 3 3 193991.4
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.673e-01 1.141e-01 4.096 4.23e-05 ***
## phi 0.000e+00 3.595e-03 0.000 1
## alpha 7.596e-01 1.808e-02 42.006 < 2e-16 ***
## a 2.390e+01 7.237e-01 33.023 < 2e-16 ***
## b 8.004e+01 2.147e+00 37.277 < 2e-16 ***
## c 1.108e+02 3.013e+00 36.762 < 2e-16 ***
## d 1.189e+00 2.983e-02 39.855 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5589 on 18741 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (27 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7164 1238.0
## 2 7163 1238.0 1 0.00 0.000 1
## 3 7154 1100.4 9 137.59 99.388 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 78202.93
## 2 2 78204.93
## 3 3 77298.20
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.118e-01 1.271e-01 1.666 0.0957 .
## phi 0.000e+00 4.599e-03 0.000 1.0000
## alpha 8.317e-01 2.587e-02 32.154 <2e-16 ***
## a 3.054e+01 2.330e+00 13.106 <2e-16 ***
## b 1.625e+02 7.450e+00 21.811 <2e-16 ***
## c 1.347e+02 9.012e+00 14.946 <2e-16 ***
## d 1.333e+00 6.538e-02 20.387 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3922 on 7154 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (9 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4868 1470.5
## 2 4867 1469.8 1 0.698 2.3127 0.1284
## 3 4860 1351.4 7 118.452 60.8552 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 52441.03
## 2 2 52440.72
## 3 3 51990.44
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.046083 0.204593 -0.225 0.8218
## phi 0.022445 0.009502 2.362 0.0182 *
## alpha 0.888690 0.039183 22.681 <2e-16 ***
## a 26.487141 1.915801 13.826 <2e-16 ***
## b 120.168676 5.959752 20.163 <2e-16 ***
## c 107.013685 5.097928 20.992 <2e-16 ***
## d 1.053641 0.051099 20.620 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5273 on 4860 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (10 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9567, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -31.414, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8771 1614.1
## 2 8770 1614.1 1 0.00 0.00 0.9999
## 3 8766 1487.3 4 126.79 186.82 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 92044.88
## 2 2 92046.88
## 3 3 91308.18
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 7.240e-02 1.103e-01 0.656 0.512
## phi 0.000e+00 5.223e-03 0.000 1.000
## alpha 7.809e-01 2.666e-02 29.292 <2e-16 ***
## a 3.121e+01 2.276e+00 13.712 <2e-16 ***
## b 1.074e+02 3.942e+00 27.247 <2e-16 ***
## c 1.078e+02 4.925e+00 21.882 <2e-16 ***
## d 1.264e+00 5.982e-02 21.138 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4119 on 8766 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (10 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12326 3355.8
## 2 12325 3355.8 1 0.00 0.0 1
## 3 12324 2995.8 1 360.03 1481.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 133924.2
## 2 2 133926.2
## 3 3 132528.8
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.758e+00 1.507e-01 11.67 <2e-16 ***
## phi 0.000e+00 4.345e-03 0.00 1
## alpha 7.243e-01 1.419e-02 51.04 <2e-16 ***
## a 2.473e+01 7.808e-01 31.68 <2e-16 ***
## b 1.068e+02 3.870e+00 27.59 <2e-16 ***
## c 1.080e+02 6.116e+00 17.66 <2e-16 ***
## d 1.475e+00 4.881e-02 30.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.493 on 12324 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (16 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12425 5068.8
## 2 12424 5065.8 1 3.00 7.3664 0.006655 **
## 3 12423 4612.3 1 453.42 1221.2549 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 137933.1
## 2 2 137927.8
## 3 3 136764.2
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.068e+00 1.492e-01 7.157 8.69e-13 ***
## phi 1.441e-02 5.553e-03 2.595 0.00948 **
## alpha 7.468e-01 1.525e-02 48.953 < 2e-16 ***
## a 2.835e+01 1.066e+00 26.591 < 2e-16 ***
## b 1.178e+02 5.361e+00 21.968 < 2e-16 ***
## c 1.222e+02 9.516e+00 12.842 < 2e-16 ***
## d 1.516e+00 6.354e-02 23.863 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6093 on 12423 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (40 observations deleted due to missingness)
## Error in nls(f_ln_3, data = G_234, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1258 341.03
## 2 1257 340.57 1 0.45741 1.6882 0.1941
## model AIC
## 1 1 14066.84
## 2 2 14067.14
## 3 3 NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.821e-02 3.664e-01 0.104 0.917
## a 1.252e+01 1.911e+01 0.655 0.512
## b 8.328e+02 2.810e+03 0.296 0.767
## c 5.000e+03 3.947e+04 0.127 0.899
## d 3.188e+00 3.021e+00 1.055 0.292
##
## Residual standard error: 0.5207 on 1258 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96304, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.433, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Error in nls(f_ln_1, data = G_242, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_242.", Mod.Sel1, sep = "")) :
## object 'nls_242.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1791 389.13
## 2 1790 389.12 1 0.015 0.0689 0.793
## 3 1789 367.65 1 21.464 104.4440 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18723.44
## 2 2 18725.38
## 3 3 18625.47
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.19924 0.32180 0.619 0.536
## phi 0.00000 0.01253 0.000 1.000
## alpha 0.74888 0.06801 11.011 < 2e-16 ***
## a 25.68778 4.97871 5.160 2.75e-07 ***
## b 100.74277 8.91977 11.294 < 2e-16 ***
## c 104.42177 8.31177 12.563 < 2e-16 ***
## d 1.14789 0.10986 10.449 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4533 on 1789 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96836, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.468, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 656 205.66
## 2 655 205.66 1 0.000 0.000 1
## 3 654 185.92 1 19.741 69.442 4.632e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6693.871
## 2 2 6695.871
## 3 3 6631.168
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.15981 0.38048 -0.420 0.675
## phi 0.00000 0.02663 0.000 1.000
## alpha 0.77294 0.08344 9.263 < 2e-16 ***
## a 20.69404 4.82816 4.286 2.09e-05 ***
## b 79.86186 9.27057 8.615 < 2e-16 ***
## c 63.52929 7.13466 8.904 < 2e-16 ***
## d 1.14819 0.15584 7.368 5.25e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5332 on 654 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94196, p-value = 2.149e-15
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.367, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Error in nls(f_ln_1, data = G_261, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_261, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_261, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) :
## object 'nls_261.' not found
simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit
unable to fit model (only 64 observations)
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) :
## object 'nls_262.' not found
simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit
unable to fit model (0 observations)
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Error in nls(f_ln_3, data = G_263, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: false convergence (8)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 149 26.638
## 2 148 26.638 1 -3.6088e-11 0 1
## model AIC
## 1 1 1935.134
## 2 2 1937.134
## 3 3 NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.224 2.254 0.543 0.5879
## a 0.000 69.109 0.000 1.0000
## b 1000.000 913.184 1.095 0.2753
## c 1898.226 4726.971 0.402 0.6886
## d 2.777 1.518 1.830 0.0693 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4228 on 149 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97748, p-value = 0.0126
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.2016, p-value = 0.0277
## alternative hypothesis: two.sided
## Error in nls(f_ln_1, data = G_313, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_313, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_313, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_313.", Mod.Sel1, sep = "")) :
## object 'nls_313.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 298 169.14
## 2 297 169.14 1 0.0000 0.0000 1.0000
## 3 296 167.90 1 1.2399 2.1858 0.1404
## model AIC
## 1 1 3100.582
## 2 2 3102.582
## 3 3 3102.353
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.4889 1.4827 0.330 0.7418
## a 0.0000 19.2900 0.000 1.0000
## b 52.4290 27.5134 1.906 0.0577 .
## c 119.8342 66.7961 1.794 0.0738 .
## d 2.1713 1.2242 1.774 0.0771 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7534 on 298 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.8809, p-value = 1.318e-14
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.2814, p-value = 3.356e-10
## alternative hypothesis: two.sided
* Cannot fit model
## Error in nls(f_ln_1, data = G_332, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_332, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_3, data = G_332, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_332$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_332.", Mod.Sel1, sep = "")) :
## object 'nls_332.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Error in nls(f_ln_1, data = G_342, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_3, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_342.", Mod.Sel1, sep = "")) :
## object 'nls_342.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6721 1270.3
## 2 6720 1264.3 1 6.032 32.06 1.557e-08 ***
## 3 6719 1085.2 1 179.120 1109.04 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 71115.80
## 2 2 71085.79
## 3 3 70060.23
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.245e-01 1.530e-01 2.775 0.00554 **
## phi 2.541e-02 5.584e-03 4.550 5.45e-06 ***
## alpha 8.215e-01 2.232e-02 36.804 < 2e-16 ***
## a 1.751e+01 2.891e+00 6.057 1.47e-09 ***
## b 1.531e+02 1.030e+01 14.864 < 2e-16 ***
## c 1.961e+02 2.327e+01 8.430 < 2e-16 ***
## d 1.631e+00 1.078e-01 15.122 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4019 on 6719 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8027 1280.2
## 2 8026 1280.2 1 0.000 0.00 1
## 3 8025 1188.2 1 92.026 621.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 88546.92
## 2 2 88548.92
## 3 3 87951.76
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 9.518e-01 1.253e-01 7.595 3.44e-14 ***
## phi 0.000e+00 4.205e-03 0.000 1
## alpha 8.478e-01 3.179e-02 26.673 < 2e-16 ***
## a 3.887e+01 2.121e+00 18.330 < 2e-16 ***
## b 1.129e+02 3.539e+00 31.916 < 2e-16 ***
## c 9.991e+01 2.742e+00 36.436 < 2e-16 ***
## d 1.168e+00 4.351e-02 26.839 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3848 on 8025 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
## Error in nls(f_ln_1, data = G_M223, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M223, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 8818.569
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -6.054e-01 2.277e-01 -2.659 0.00798 **
## phi 7.662e-02 1.800e-02 4.257 2.3e-05 ***
## alpha 8.905e-01 7.124e-02 12.500 < 2e-16 ***
## a 0.000e+00 4.759e+01 0.000 1.00000
## b 3.440e+02 6.861e+02 0.501 0.61621
## c 1.654e+03 1.060e+04 0.156 0.87595
## d 3.294e+00 3.719e+00 0.886 0.37607
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3373 on 875 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96709, p-value = 3.239e-13
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.555, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Error in nls(f_ln_1, data = G_M231, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M231, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 10131.35
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.135e-01 5.352e-01 0.959 0.3376
## phi 7.733e-03 2.242e-02 0.345 0.7302
## alpha 7.642e-01 7.743e-02 9.870 <2e-16 ***
## a 1.667e+01 8.120e+00 2.053 0.0404 *
## b 1.758e+02 1.157e+02 1.519 0.1290
## c 4.206e+02 6.048e+02 0.695 0.4869
## d 2.147e+00 8.579e-01 2.502 0.0125 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.453 on 980 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96207, p-value = 2.47e-15
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.989, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3172 1918.7
## 2 3171 1918.7 1 0.00 0.0000 1
## 3 3148 1790.5 23 128.11 9.7928 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 41988.35
## 2 2 41990.35
## 3 3 41548.04
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.18061 0.49156 -0.367 0.713331
## phi 0.00000 0.01505 0.000 1.000000
## alpha 1.10192 0.06873 16.033 < 2e-16 ***
## a 3.55424 13.98067 0.254 0.799338
## b 568.48059 92.86868 6.121 1.04e-09 ***
## c 667.30946 174.01443 3.835 0.000128 ***
## d 2.21626 0.22808 9.717 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7542 on 3148 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (24 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95105, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -17.577, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1952 1001.42
## 2 1951 925.67 1 75.745 159.6441 < 2.2e-16 ***
## 3 1935 894.94 16 30.737 4.1537 5.856e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24765.07
## 2 2 24613.15
## 3 3 24401.78
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91612, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.034, p-value = 0.002414
## alternative hypothesis: two.sided
## Warning in mean.default(G_M261$MEASTIM, na.rm = TE): argument is not numeric or
## logical: returning NA
## Warning: Removed 1000 row(s) containing missing values (geom_path).
## Warning: Removed 20 rows containing missing values (geom_point).
## Warning: Removed 20 rows containing missing values (geom_pointrange).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 356 110.33
## 2 355 109.15 1 1.1717 3.8108 0.051710 .
## 3 354 105.62 1 3.5361 11.8518 0.000645 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3771.802
## 2 2 3769.947
## 3 3 3760.059
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.81573 0.33677 -5.392 1.28e-07 ***
## phi 0.04237 0.02511 1.688 0.092361 .
## alpha 0.50499 0.13502 3.740 0.000214 ***
## a 54.76880 15.65852 3.498 0.000529 ***
## b 184.32447 40.04085 4.603 5.80e-06 ***
## c 158.85154 25.00796 6.352 6.53e-10 ***
## d 0.81683 0.15947 5.122 4.97e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5462 on 354 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94156, p-value = 9.985e-11
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.18153, p-value = 0.856
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1691 583.39
## 2 1690 583.09 1 0.308 0.8923 0.345
## 3 1689 527.98 1 55.108 176.2917 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17699.64
## 2 2 17700.75
## 3 3 17534.37
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.07060 0.29359 -3.647 0.000274 ***
## phi 0.01782 0.01162 1.534 0.125224
## alpha 0.64315 0.04157 15.472 < 2e-16 ***
## a 41.57156 5.51472 7.538 7.73e-14 ***
## b 135.46943 16.29218 8.315 < 2e-16 ***
## c 212.14212 23.03599 9.209 < 2e-16 ***
## d 1.23436 0.11259 10.963 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5591 on 1689 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (15 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92964, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.9597, p-value = 7.058e-07
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2641 1154.9
## 2 2640 1151.5 1 3.413 7.8251 0.00519 **
## 3 2617 1078.3 23 73.212 7.7253 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 28864.48
## 2 2 28858.65
## 3 3 28506.38
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.73312 0.75925 0.966 0.33434
## phi 0.03805 0.01345 2.828 0.00472 **
## alpha 0.63197 0.04647 13.598 < 2e-16 ***
## a 25.71790 4.64424 5.538 3.37e-08 ***
## b 99.70475 17.65984 5.646 1.82e-08 ***
## c 210.36985 18.10340 11.620 < 2e-16 ***
## d 1.24064 0.09401 13.197 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6419 on 2617 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (25 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89938, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.6907, p-value = 2.722e-06
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1665 654.15
## 2 1664 653.64 1 0.511 1.3008 0.2542
## 3 1663 607.37 1 46.266 126.6784 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18742.43
## 2 2 18743.13
## 3 3 18622.53
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.49946 1.96354 1.273 0.20322
## phi 0.01486 0.01732 0.858 0.39089
## alpha 0.70768 0.05537 12.781 < 2e-16 ***
## a 17.72088 5.65869 3.132 0.00177 **
## b 88.45316 27.94636 3.165 0.00158 **
## c 132.83193 5.59014 23.762 < 2e-16 ***
## d 0.97930 0.04976 19.680 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6043 on 1663 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (5 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93649, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.1382, p-value = 3.5e-05
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 356 147.67
## 2 355 146.35 1 1.3214 3.2053 0.07425 .
## 3 354 127.38 1 18.9706 52.7223 2.459e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3622.910
## 2 2 3621.665
## 3 3 3573.547
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.030e+00 4.880e-01 -2.111 0.0355 *
## phi 5.401e-03 3.136e-02 0.172 0.8633
## alpha 7.993e-01 9.457e-02 8.452 7.54e-16 ***
## a 0.000e+00 7.695e+01 0.000 1.0000
## b 1.379e+02 2.192e+02 0.629 0.5295
## c 7.728e+02 4.021e+03 0.192 0.8477
## d 3.138e+00 4.935e+00 0.636 0.5253
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5999 on 354 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94196, p-value = 1.11e-10
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.6772, p-value = 2.436e-11
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 207 64.472
## 2 206 64.472 1 0.0000 0.000 0.9999985
## 3 205 60.643 1 3.8286 12.942 0.0004027 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2088.502
## 2 2 2090.502
## 3 3 2079.523
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.88598 0.37590 -5.017 1.13e-06 ***
## phi 0.00000 0.05799 0.000 1.000000
## alpha 0.50427 0.12433 4.056 7.10e-05 ***
## a 36.45861 9.41288 3.873 0.000144 ***
## b 126.50101 26.04280 4.857 2.36e-06 ***
## c 150.15616 16.92871 8.870 3.62e-16 ***
## d 0.93149 0.16914 5.507 1.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5439 on 205 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93284, p-value = 2.735e-08
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.89551, p-value = 0.3705
## alternative hypothesis: two.sided
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3 |
| 212 | Laurentian Mixed Forest | 3 |
| 221 | Eastern Broadleaf Forest | 3 |
| 222 | Midwest Broadleaf Forest | 3 |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3 |
| 232 | Outer Coastal Plain Mixed Forest | 3 |
| 234 | Lower Mississippi Riverine Forest | 1 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 3 |
| 255 | Prairie Parkland (Subtropical) | 3 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 1 |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | 1 |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3 |
| M242 | Cascade Mixed Forest | 3 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 3 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 3 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 3 |
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6806 | 2847 | 0.5614145 | 0.1577549 | 0.9650741 | 0.0098539 | -0.0024099 | 0.0221177 | 0.8464830 | 0.7930648 | 0.8999011 | 40.304388 | 36.5067722 | 44.10200 | 107.31646 | 97.512853 | 117.12006 | 114.42661 | 106.29574 | 122.55748 | 0.9189999 | 0.8412571 | 0.9967427 |
| 212 | Laurentian Mixed Forest | east | 18775 | 8891 | 0.4673302 | 0.2436774 | 0.6909831 | 0.0000000 | -0.0070458 | 0.0070458 | 0.7596243 | 0.7241785 | 0.7950701 | 23.899941 | 22.4813449 | 25.31854 | 80.03947 | 75.830899 | 84.24804 | 110.76006 | 104.85445 | 116.66568 | 1.1888448 | 1.1303764 | 1.2473132 |
| 221 | Eastern Broadleaf Forest | east | 7170 | 3490 | 0.2118160 | -0.0373764 | 0.4610084 | 0.0000000 | -0.0090147 | 0.0090147 | 0.8317337 | 0.7810259 | 0.8824414 | 30.540702 | 25.9727555 | 35.10865 | 162.50411 | 147.899022 | 177.10920 | 134.68414 | 117.01892 | 152.34937 | 1.3329128 | 1.2047471 | 1.4610786 |
| 222 | Midwest Broadleaf Forest | east | 4877 | 2401 | -0.0460834 | -0.4471784 | 0.3550117 | 0.0224450 | 0.0038175 | 0.0410725 | 0.8886905 | 0.8118750 | 0.9655059 | 26.487141 | 22.7313038 | 30.24298 | 120.16868 | 108.484868 | 131.85248 | 107.01369 | 97.01944 | 117.00793 | 1.0536407 | 0.9534643 | 1.1538171 |
| 223 | Central Interior Broadleaf Forest | east | 8783 | 3725 | 0.0724004 | -0.1438177 | 0.2886185 | 0.0000000 | -0.0102390 | 0.0102390 | 0.7809249 | 0.7286645 | 0.8331854 | 31.207745 | 26.7462045 | 35.66929 | 107.40334 | 99.676437 | 115.13025 | 107.77584 | 98.12105 | 117.43062 | 1.2644153 | 1.1471617 | 1.3816690 |
| 231 | Southeastern Mixed Forest | east | 12347 | 5691 | 1.7584838 | 1.4630660 | 2.0539017 | 0.0000000 | -0.0085177 | 0.0085177 | 0.7243199 | 0.6965018 | 0.7521381 | 24.733949 | 23.2034139 | 26.26448 | 106.78132 | 99.195302 | 114.36733 | 107.97366 | 95.98608 | 119.96123 | 1.4752723 | 1.3795973 | 1.5709472 |
| 232 | Outer Coastal Plain Mixed Forest | east | 12470 | 6101 | 1.0680057 | 0.7755160 | 1.3604953 | 0.0144070 | 0.0035228 | 0.0252912 | 0.7467943 | 0.7168913 | 0.7766972 | 28.350008 | 26.2601723 | 30.43984 | 117.77229 | 107.263792 | 128.28078 | 122.20351 | 103.55149 | 140.85553 | 1.5162934 | 1.3917433 | 1.6408436 |
| 234 | Lower Mississippi Riverine Forest | east | 1265 | 714 | 0.0382065 | -0.6806976 | 0.7571107 | NA | NA | NA | NA | NA | NA | 12.524348 | -24.9680876 | 50.01678 | 832.84146 | -4680.032010 | 6345.71492 | 5000.00000 | -72429.65447 | 82429.65447 | 3.1877269 | -2.7399232 | 9.1153769 |
| 242 | Pacific Lowland Mixed Forest | pacific | 81 | 81 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1797 | 809 | 0.1992410 | -0.4319029 | 0.8303849 | 0.0000000 | -0.0245663 | 0.0245663 | 0.7488833 | 0.6154953 | 0.8822713 | 25.687780 | 15.9230754 | 35.45248 | 100.74277 | 83.248507 | 118.23703 | 104.42177 | 88.11996 | 120.72357 | 1.1478928 | 0.9324216 | 1.3633639 |
| 255 | Prairie Parkland (Subtropical) | pacific | 663 | 293 | -0.1598090 | -0.9069202 | 0.5873022 | 0.0000000 | -0.0522822 | 0.0522822 | 0.7729398 | 0.6090928 | 0.9367868 | 20.694043 | 11.2134875 | 30.17460 | 79.86186 | 61.658187 | 98.06554 | 63.52929 | 49.51970 | 77.53889 | 1.1481892 | 0.8421804 | 1.4541980 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 24 | 24 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 155 | 155 | 1.2239516 | -3.2300182 | 5.6779213 | NA | NA | NA | NA | NA | NA | 0.000000 | -136.5600679 | 136.56007 | 1000.00000 | -804.464574 | 2804.46457 | 1898.22617 | -7442.33100 | 11238.78334 | 2.7771137 | -0.2216429 | 5.7758703 |
| 313 | Colorado Plateau Semi-Desert | interior west | 215 | 215 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 304 | 240 | 0.4888930 | -2.4290839 | 3.4068698 | NA | NA | NA | NA | NA | NA | 0.000000 | -37.9618826 | 37.96188 | 52.42899 | -1.716234 | 106.57421 | 119.83421 | -11.61767 | 251.28608 | 2.1713420 | -0.2377897 | 4.5804737 |
| 332 | Great Plains Steppe | interior west | 195 | 106 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | interior west | 62 | 62 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 121 | 120 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 93 | 61 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6729 | 2989 | 0.4244549 | 0.1245744 | 0.7243355 | 0.0254110 | 0.0144641 | 0.0363579 | 0.8214671 | 0.7777125 | 0.8652217 | 17.506687 | 11.8403129 | 23.17306 | 153.07530 | 132.887777 | 173.26283 | 196.14427 | 150.53438 | 241.75416 | 1.6306139 | 1.4192376 | 1.8419902 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8034 | 3700 | 0.9517694 | 0.7061059 | 1.1974328 | 0.0000000 | -0.0082433 | 0.0082433 | 0.8478212 | 0.7855128 | 0.9101296 | 38.871490 | 34.7143586 | 43.02862 | 112.93446 | 105.998009 | 119.87091 | 99.91458 | 94.53922 | 105.28995 | 1.1678540 | 1.0825568 | 1.2531512 |
| M223 | Ozark Broadleaf Forest Meadow | east | 883 | 343 | -0.6053958 | -1.0522432 | -0.1585484 | 0.0766208 | 0.0412940 | 0.1119475 | 0.8905107 | 0.7506879 | 1.0303336 | 0.000000 | -93.3960670 | 93.39607 | 343.99698 | -1002.514773 | 1690.50873 | 1654.41165 | -19140.77724 | 22449.60055 | 3.2937215 | -4.0057665 | 10.5932095 |
| M231 | Ouachita Mixed Forest | east | 988 | 481 | 0.5134884 | -0.5368625 | 1.5638393 | 0.0077329 | -0.0362649 | 0.0517307 | 0.7642262 | 0.6122847 | 0.9161677 | 16.669136 | 0.7341976 | 32.60408 | 175.75451 | -51.246800 | 402.75582 | 420.56722 | -766.18859 | 1607.32303 | 2.1467388 | 0.4631696 | 3.8303080 |
| M242 | Cascade Mixed Forest | pacific | 3179 | 3176 | -0.1806076 | -1.1444145 | 0.7831992 | 0.0000000 | -0.0295146 | 0.0295146 | 1.1019213 | 0.9671674 | 1.2366752 | 3.554237 | -23.8579198 | 30.96639 | 568.48059 | 386.391317 | 750.56986 | 667.30946 | 326.11626 | 1008.50266 | 2.2162649 | 1.7690691 | 2.6634607 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1963 | 1963 | 0.0592276 | -1.1060519 | 1.2245071 | 0.1887636 | 0.1653016 | 0.2122257 | 0.7151681 | 0.5373863 | 0.8929498 | 0.000000 | -49.7841398 | 49.78414 | 505.48187 | 249.528689 | 761.43505 | 905.74901 | -314.98988 | 2126.48791 | 2.7254405 | 1.6285474 | 3.8223335 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 19 | 19 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 362 | 362 | -1.8157315 | -2.4780584 | -1.1534046 | 0.0423700 | -0.0070057 | 0.0917456 | 0.5049877 | 0.2394459 | 0.7705295 | 54.768802 | 23.9733782 | 85.56423 | 184.32447 | 105.576614 | 263.07233 | 158.85154 | 109.66869 | 208.03438 | 0.8168324 | 0.5032028 | 1.1304621 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1711 | 1711 | -1.0705976 | -1.6464275 | -0.4947678 | 0.0178205 | -0.0049652 | 0.0406063 | 0.6431528 | 0.5616230 | 0.7246825 | 41.571559 | 30.7551625 | 52.38796 | 135.46943 | 103.514440 | 167.42443 | 212.14212 | 166.96002 | 257.32422 | 1.2343633 | 1.0135251 | 1.4552014 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2649 | 2648 | 0.7331242 | -0.7556754 | 2.2219239 | 0.0380474 | 0.0116674 | 0.0644274 | 0.6319656 | 0.5408357 | 0.7230954 | 25.717902 | 16.6111486 | 34.82465 | 99.70475 | 65.076091 | 134.33342 | 210.36985 | 174.87141 | 245.86829 | 1.2406376 | 1.0563039 | 1.4249713 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1675 | 1675 | 2.4994612 | -1.3518126 | 6.3507349 | 0.0148648 | -0.0191073 | 0.0488368 | 0.7076774 | 0.5990745 | 0.8162802 | 17.720879 | 6.6219799 | 28.81978 | 88.45316 | 33.639406 | 143.26692 | 132.83193 | 121.86747 | 143.79639 | 0.9793045 | 0.8817043 | 1.0769048 |
| M334 | Black Hills Coniferous Forest | interior west | 362 | 170 | -1.0302125 | -1.9899535 | -0.0704714 | 0.0054010 | -0.0562644 | 0.0670664 | 0.7993264 | 0.6133402 | 0.9853125 | 0.000000 | -151.3293796 | 151.32938 | 137.94375 | -293.146235 | 569.03374 | 772.76960 | -7135.30221 | 8680.84140 | 3.1376453 | -6.5672504 | 12.8425411 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 213 | 213 | -1.8859784 | -2.6271118 | -1.1448450 | 0.0000000 | -0.1143395 | 0.1143395 | 0.5042656 | 0.2591273 | 0.7494039 | 36.458606 | 17.9001475 | 55.01706 | 126.50101 | 75.154935 | 177.84709 | 150.15616 | 116.77947 | 183.53286 | 0.9314925 | 0.5980113 | 1.2649737 |
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: Removed 15 rows containing missing values (geom_point).
## Warning: Removed 12 rows containing missing values (geom_point).
## Warning: Removed 15 rows containing missing values (geom_point).
## Warning: Removed 12 rows containing missing values (geom_point).
## region weighted.ge
## 1 entire US 0.55968415
## 2 pacific -0.05524554
## 3 east 0.66740389
## 4 interior west 0.42071032
## region weighted.phi
## 1 entire US 0.014754084
## 2 pacific 0.065098909
## 3 east 0.006528787
## 4 interior west 0.022812632
## region weighted.alpha
## 1 entire US 0.7600027
## 2 pacific 0.9012734
## 3 east 0.7731147
## 4 interior west 0.5803015
## region weighted.ge
## 1 entire US 0.62621417
## 2 pacific -0.08899515
## 3 east 0.71149013
## 4 interior west 0.73312423
## region weighted.phi
## 1 entire US 0.014572771
## 2 pacific 0.072104104
## 3 east 0.005578167
## 4 interior west 0.038047400
## region weighted.alpha
## 1 entire US 0.7799773
## 2 pacific 0.9541889
## 3 east 0.7673245
## 4 interior west 0.6319656